Macroscopically local correlations can violate information causality

Abstract: Although quantum mechanics is a very successful theory, its foundations are still a subject of intense debate. One of the main problems is the fact that quantum mechanics is based on abstract mathematical axioms, rather than on physical principles. Quantum information theory has recently provided new ideas from which one could obtain physical axioms constraining the resulting statistics one can obtain in experiments. Information causality and macroscopic locality are two principles recently proposed to solve this problem. However none of them were proven to define the set of correlations one can observe. In this paper, we present an extension of information causality and study its consequences. It is shown that the two above-mentioned principles are inequivalent: if the correlations allowed by nature were the ones satisfying macroscopic locality, information causality would be violated. This gives more confidence in information causality as a physical principle defining the possible correlation allowed by nature.